If you draw an imaginary line from your eye to the water droplet
in the sky, and then another line back toward the sun's position
in the sky, the angle between those two lines must equal 42
degrees for a rainbow to appear.

A double rainbow -- one on top of another -- occurs when sunlight
bounces back and forth twice inside the same rain drop before
being reflected back to the observer.

A twinned rainbow appears to be two rainbows splitting from the
base of a single one. That's the subject of the paper by Sadeghi
and others at UCSD.

Henrik Jensen, professor of computer science and engineering at
UCSD and a co-author, said he's been looking at simulating
rainbows on a computer for the past few years. Although the
origin of rainbows has been understood since French philosopher
and mathematician Rene Descartes wrote about them in 1637, the
ability to model them on a computer is more recent.

"We started out looking at what would cause rainbows," Jensen
said, "and how could we capture rainbows in nature using computer
graphics."

Jensen said that as raindrops fall through the air, they begin to
flatten at their bottom. That hamburger-like shape -- known as a
"burgeroid" -- affects how sunlight reflects back out and toward
the viewer. Earlier simulated rainbows had only used
spherical-shaped droplets, said Jensen.

As they started running various simulations, the scientists
realized that the interaction of light with spherical drops could
not explain some kinds of rainbows, such as twinned rainbows.

The UCSD team made all kinds of different virtual rainbows using
computer simulations, (some took six to eight hours to create)
which are available on their Flickr
website.

"From a graphics point of view this looks very interesting," said
Jerry Tessendorf, a computer graphics expert who teachers digital
production at Clemson University.

UCSD's Jensen said the film and television industry is always
interested in simulating reality (he worked on James Cameron's
"Avatar" while Sadeghi worked on Disney's "Tangled"), and that
rainbows have been difficult to get just right. The team's new
finding should make that easier -- although its still not going
to enough to build a rainbow machine.

"That would be difficult," Sadeghi said. "You would have to
control the shape of the water drops that are falling in the
air."